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31.
A triangular lattice model for pattern formation by core-shell particles at fluid interfaces is introduced and studied for the particle to core diameter ratio equal to 3. Repulsion for overlapping shells and attraction at larger distances due to capillary forces are assumed. Ground states and thermodynamic properties are determined analytically and by Monte Carlo simulations for soft outer- and stiffer inner shells, with different decay rates of the interparticle repulsion. We find that thermodynamic properties are qualitatively the same for slow and for fast decay of the repulsive potential, but the ordered phases are stable for temperature ranges, depending strongly on the shape of the repulsive potential. More importantly, there are two types of patterns formed for fixed chemical potential—one for a slow and another one for a fast decay of the repulsion at small distances. In the first case, two different patterns—for example clusters or stripes—occur with the same probability for some range of the chemical potential. For a fixed concentration, an interface is formed between two ordered phases with the closest concentration, and the surface tension takes the same value for all stable interfaces. In the case of degeneracy, a stable interface cannot be formed for one out of four combinations of the coexisting phases, because of a larger surface tension. Our results show that by tuning the architecture of a thick polymeric shell, many different patterns can be obtained for a sufficiently low temperature. 相似文献
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Viktor Gerasimenko Vyacheslav Shtyk Anatoly Zagorodny 《Central European Journal of Physics》2011,9(1):71-77
Evolution equations for marginal generalized microscopic phase densities are introduced. The evolution equations for average
values of microscopic phase densities are derived and a solution of the initial-value problem for the hydrodynamic type hierarchy
obtained is constructed. 相似文献
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On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains 总被引:8,自引:0,他引:8
The restrictions Bspq() and Fspq() of the Besov and TriebelLizorkinspaces of tempered distributions Bspq(Rn) and Fspq(Rn) to Lipschitzdomains Rn are studied. For general values of parameters (sR,p>0, q>0) a universal linear bounded extensionoperator from Bspq() and Fspq() into the corresponding spaceson Rn is constructed. The construction is based on a new variantof the Calderón reproducing formula with kernels supportedin a fixed cone. Explicit characterizations of the elementsof Bspq() and Fspq() in terms of their values in are also obtained. 相似文献
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Perfluorinated benzocycloalkenes (benzocyclobutene, indan, tetralin), alkylbenzocycloalkenes and alkylbenzenes react with CF3COOH/SbF5 at 20-50 °C giving the corresponding carbonyl derivatives. 相似文献
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Ivan?DimitrovEmail author Vyacheslav?Futorny Ivan?Penkov 《Communications in Mathematical Physics》2004,250(1):47-63
Let be a toroidal Lie algebra corresponding to a semisimple Lie algebra We describe all Borel subalgebras of which contain the Cartan subalgebra where is a fixed Cartan subalgebra of We show that each such Borel subalgebra determines a parabolic decomposition where is a proper toroidal subalgebra of and Our first main result is that, for any weight which does not vanish on , an arbitrary subquotient of the Verma module is induced from its submodule of invariant vectors. This reduces the study of subquotients of to the study of subquotients of Verma modules over . We then introduce categories and and their respective blocks and corresponding to a central charge which is nonzero on . Our second main result is that the functors of induction and invariants are mutually inverse equivalences of the category and the full subcategory of whose objects are generated by their invariants. 相似文献